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arXiv · 2311.05834

An upper bound of the Hausdorff dimension of singular vectors on affine subspaces

Nimish A. Shah·Pengyu Yang
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Abstract

In Diophantine approximation, the notion of singular vectors was introduced by Khintchine in the 1920's. We study the set of singular vectors on an affine subspace of $\mathbb{R}^n$. We give an upper bound of its Hausdorff dimension in terms of the Diophantine exponent of the parameter of the affine subspace.

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Nimish A. Shah, Pengyu Yang. 2023-11-10. An upper bound of the Hausdorff dimension of singular vectors on affine subspaces. https://doi.org/10.1090/btran%2F212

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